Mental and physical aspects are both integral to health but little is known about the dynamic relationship between them. We consider the dynamic relationship between mental and physical health using a sample of 11,203 individuals in six waves (2002-2013) of the English Longitudinal Study of Ageing (ELSA). We estimate conditional linear and non-linear random-effects regression models to identify the effects of past physical health, measured by Activities of Daily Living (ADL), and past mental health, measured by the Centre for Epidemiological Studies Depression (CES-D) scale, on both present physical and mental health. We find that both mental and physical health are moderately state-dependent. Better past mental health increases present physical health significantly. Better past physical health has a larger effect on present mental health. Past mental health has stronger effects on present physical health than physical activity or education. It explains 2.0% of the unobserved heterogeneity in physical health. Past physical health has stronger effects on present mental health than health investments, income or education. It explains 0.4% of the unobserved heterogeneity in mental health. These cross-effects suggest that health policies aimed at specific aspects of health should consider potential spill-over effects.